ODE
\[ y(x) (a+b x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00841147 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_1 \text {Ai}\left (-\frac {a+b x}{(-b)^{2/3}}\right )+c_2 \text {Bi}\left (-\frac {a+b x}{(-b)^{2/3}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.115 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm Ai}\left (-{(bx+a){b}^{-{\frac {2}{3}}}}\right )}+{\it \_C2}\,{{\rm Bi}\left (-{(bx+a){b}^{-{\frac {2}{3}}}}\right )} \right \} \] Mathematica raw input
DSolve[(a + b*x)*y[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> AiryAi[-((a + b*x)/(-b)^(2/3))]*C[1] + AiryBi[-((a + b*x)/(-b)^(2/3))]*C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+(b*x+a)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*AiryAi(-1/b^(2/3)*(b*x+a))+_C2*AiryBi(-1/b^(2/3)*(b*x+a))